Cook, S.A., "Linear time simulation of deterministic two-way pushdown automata," pp. 172-179 in Information Processing 71: Proceedings of the IFIP Congress 71, ed. C.V. Freiman,North-Holland, Amsterdam (1972). - 12 -  Home/Search   Document Not in Database   Summary   Related Articles   Check

....promised in section 3.4 and section 5.3, we now present a realistic program which by means of ultimate sharing can be made to run exponentially faster. The program to be considered is a simulator for two way deterministic pushdown automata (2DPDA) AHU74, chap. 9] It caused much surprise when [Coo71] showed that it is always possible to simulate a 2DPDA in linear time (wrt. the length of the input tape) even if the automaton carries out an exponential number of steps in particular this result gave Donald Knuth inspiration to his fast substring matching algorithm [KMP77, p. 338] We shall ....

....theorem 6.3.2 where we know c = 8 can be used) can deduce that # loops on # . Another way to detect loops would be to keep track of whether the 2DM twice performs a PUSH step pushing the same expression. 6. 5 Previous work The original technique for linear time simulation of a 2DPDA, used in [Coo71] and restated as [AHU74, algorithm 9.4] is a bottom up approach (cf. page 20) We will now hint at how to translate this method into our As no infinite sequence of PUSH steps is possible, fact 5.1.2 tells us that the 2DM loops i# can become arbitrarily big. 157 framework: given an ....

Stephen A. Cook. Linear time simulation of deterministic two-way pushdown automata. In Information Processing 71. Proceedings of IFIP Congress 1971, pages 75--80. NorthHolland, 1971.

....itself cannot be used to prove this direction. The reason is that each node requires space O(log(n) because under the assumption of a potentially infinite heap we must allow space O(log(n) to store a pointer. In order to assess the expressive power of the full system we use the following result [7] due to Stephen Cook 3 [7] Theorem 5.2 (Cook) The following are equivalent for a function f : N # N i) f(x) is computable in time O(2 c x ) for some c, ii) f(x) is computable by a O( x ) space bounded Turing machine having as extra resource an unbounded stack. The stack can e.g. be ....

....this direction. The reason is that each node requires space O(log(n) because under the assumption of a potentially infinite heap we must allow space O(log(n) to store a pointer. In order to assess the expressive power of the full system we use the following result [7] due to Stephen Cook 3 [7]. Theorem 5.2 (Cook) The following are equivalent for a function f : N # N i) f(x) is computable in time O(2 c x ) for some c, ii) f(x) is computable by a O( x ) space bounded Turing machine having as extra resource an unbounded stack. The stack can e.g. be formalised as a one side ....

Stephen A. Cook. Linear-time simulation of deterministic two-way pushdown automata. Information Processing, 71:75--80, 1972.

....forth, moving the a to the left and the b to the right, until after j steps the a arrives at the to the left of its original position. The b is now j sites to the right of the appropriate . Surprisingly, Acceptance for deterministic two way PDA s in one dimension is decidable in linear time [7], so we have Corollary. Acceptance for deterministic PDA s in any number of dimensions can be decided in time proportional to the volume. There are several higher types of recognizers that the reader should be aware of if she wishes to further explore this subject, such as: Alternating Finite ....

S.A. Cook, \Linear time simulation of deterministic two-way pushdown automata." Proc. 1971 IFIP Congress 75-80.

....years have seen marked dissatisfaction with the computational realism of the classic machine models, such as Turing machines or the standard integer RAM (see [13, 12] Many algorithms that theoretically run in linear time on the RAM scale non linearly when it comes time to implement them. Cook [5, 6] proposed replacing the usual unit cost RAM measure by the log cost criterion, by which an operation that reads an integer i stored at address a is charged log i log a time units. Aggarwal, Alpern, Chandra, and Snir [1] went further by introducing a parameter : N N called a memory access cost ....

S. Cook. Linear time simulation of deterministic two-way pushdown automata. In Proceedings, IFIP '71, pages 75--80. North--Holland, 1971.

....Galil [11] and Slisenko [18] presented real time initial palindrome recognition algorithms for multi tape Turing machines. It is interesting to note that the existence of efficient algorithms that find initial palindromes in a string was also implied by theoretical results on fast simulation [6, 10]. Knuth, Morris and Pratt [15] gave another linear time algorithm that finds all initial palindromes in a string. A closer look at Manacher s algorithm shows that it not only finds the initial palindromes, but it also computes the maximal radii of palindromes centered at all positions of the input ....

S.A. Cook. Linear time simulation of deterministic two-way pushdown automata. In Information Processing 71, pages 75--80. North Holland Publishing Co., Amsterdam, the Netherlands, 1972.

....back to 1969 when Morris implemented an early version of the algorithm in a text editor for the CDC 6400 computer. The discovery of the algorithm has a very interesting history as reported in the paper [66] that was published only in 1977. Most notable probably is the fact that a result of Cook [33] on linear time simulation of two way deterministic pushdown automaton by a random access machine implied that a lineartime string matching algorithm exists. Knuth went through the laborious details of Cook s construction and discovered the algorithm. The algorithm reported in the final paper is a ....

S. A. Cook. Linear time simulation of deterministic two-way pushdown automata. In Information Processing 71, pages 75--80. North Holland Publishing Co., Amsterdam, the Netherlands, 1972.

....3 See [5] p. 61, where this is done for finite automata. This is valid, since a deterministic pushdown automaton can have at most one permitted transition for a given combination of state, head position, and stack symbol. Xi A linear time algorithm for simulating a 2DPDA was found by Cook [3], so the above theorem does not improve on known results. It would be interesting to know whether an analogue of theorem (7) holds i.e. whether monadic congruence closure can be solved by a 2DPDA. Discussion The class NC of problems solvable in polylogarithmic (O(log k n) time using a ....

Cook, S. A. (1971) Linear time simulation of deterministic two-way pushdown automata, Proceedings of the 1971 IFIP Congress, pp. 75-80.

....consistency of a single coded method, assuming covariance, is in DLOGSPACE and can be checked in O(n c) time. We present a first principles algorithm to show this linear time bound using radix trees. Initially, we showed this bound using two way deterministic pushdown automata (2dpda s) [9]. We present this proof in an appendix. In the case of recursion free schemas, the consistency problem is coNP complete for a single coded method with two arguments. Some special cases can be shown to be in PTIME, using tree automata techniques [11, 31] Covariance does not help in the recursive ....

S.A. Cook. Linear-time Simulation of Deterministic Two-way Pushdown Automata. Proc. IFIP Congress, 172--179, 1971.

....alopez o maytag.UWaterloo.ca 1 Introduction In 1970, Knuth, Morris, and Pratt proposed their famous linear time pattern matching algorithm for two strings. Their algorithm was derived from a result of Cook that 2 way deterministic pushdown languages are recognizable on a RAM in linear time [Co71]. In 1973, Weiner [PeWe73] presented a very original algorithm that performs linear time recognition of repeated instances of a substring in a string. Weiner s approach to this problem was as important as the solution to the problem itself. The relevance of his work was immediately appreciated. ....

S.A. Cook, Linear time simulation of deterministic two-way pushdown automata. Proceedings of IFIP Congress, North-Holland, 1971.

....forth, moving the a to the left and the b to the right, until after j steps the a arrives at the to the left of its original position. The b is now j sites to the right of the appropriate . Surprisingly, Acceptance for deterministic two way PDA s in one dimension is decidable in linear time [7], so we have Corollary. Acceptance for deterministic PDA s in any number of dimensions can be decided in time proportional to the volume. There are several higher types of recognizers that the reader should be aware of if she wishes to further explore this subject, such as: Alternating Finite ....

S.A. Cook, "Linear time simulation of deterministic two-way pushdown automata." Proc. 1971 IFIP Congress 75--80.

....consistency of a single coded method, assuming covariance, is in DLOGSPACE and can be checked in O(n c) time. We present a first principles algorithm to show this linear time bound using radix trees. Initially, we showed this bound using two way deterministic pushdown automata (2dpda s) [9]. We present this proof in an appendix. In the case of recursion free schemas, the consistency problem is coNP complete for a single coded method with two arguments. Some special cases can be shown to be in PTIME, using tree automata techniques [11, 32] Covariance does not help in the recursive ....

S.A. Cook. Linear-time Simulation of Deterministic Two-way Pushdown Automata. Proc. IFIP Congress, 172--179, 1971.

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Cook, S.A., "Linear time simulation of deterministic two-way pushdown automata," pp. 172-179 in Information Processing 71: Proceedings of the IFIP Congress 71, ed. C.V. Freiman,North-Holland, Amsterdam (1972). - 12 -

No context found.

Cook, S.A., "Linear time simulation of deterministic two-way pushdown automata," pp. 172-179 in Information Processing 71: Proc. of the IFIP Congress 71, ed. C.V. Freiman,North-Holland, Amsterdam (1972).

No context found.

S. A. Cook, Linear-time simulation of deterministic two-way pushdown automata, Information Processing (IFIP) 71, C.V. Freiman, (ed.), NorthHolland, pp. 75--80, 1971.

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S. A. Cook, Linear-time simulation of deterministic two-way pushdown automata, Information Processing (IFIP) 71, C.V. Freiman, (ed.), North-Holland, pp. 75--80, 1971.

No context found.

S. Cook, Linear Time Simulation of Deterministic Two-Way Pushdown Automata, Proc. IFIP Congress 1971, C. Freiman Ed., North-Holland, Amsterdam (1971), pp. 75--80.

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